reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th23:
  for f being Function of Seg i, D holds f is FinSequence of D
proof
  let f be Function of Seg i, D;
  reconsider i as Element of NAT by ORDINAL1:def 12;
  dom f = Seg i by FUNCT_2:def 1;
  then
A1: f is FinSequence by FINSEQ_1:def 2;
  rng f c= D by RELAT_1:def 19;
  hence thesis by A1,FINSEQ_1:def 4;
end;
